Editing New riddle of induction (section)

==The new riddle of induction==
In this section, Goodman's new riddle of induction is outlined in order to set the context for his introduction of the predicates ''grue'' and ''bleen'' and thereby illustrate their [[Philosophy|philosophical importance]].{{sfn|Goodman|1983|p=74}}<ref name="Godfrey-Smith">{{cite book|author=Peter Godfrey-Smith|title=Theory and Reality|url=http://www.press.uchicago.edu|access-date=23 October 2012|year=2003|publisher=University of Chicago Press|isbn=978-0-226-30063-4|page=53}}</ref>

===The old problem of induction and its dissolution===
Goodman poses [[Hume's problem of induction]] as a problem of the validity of the [[prediction]]s we make.  Since predictions are about what has yet to be observed and because there is no necessary connection between what has been observed and what will be observed, there is no objective justification for these predictions.  Deductive logic cannot be used to infer predictions about future observations based on past observations because there are no valid rules of deductive logic for such inferences.  Hume's answer was that observations of one kind of event following another kind of event result in habits of regularity (i.e., associating one kind of event with another kind).  Predictions are then based on these regularities or habits of mind.

Goodman takes Hume's answer to be a serious one.  He rejects other philosophers' objection that Hume is merely explaining the origin of our predictions and not their justification.  His view is that Hume has identified something deeper.  To illustrate this, Goodman turns to the problem of justifying a [[Deductive system|system of rules of deduction]].  For Goodman, the validity of a deductive system is justified by its conformity to good deductive practice.  The justification of rules of a deductive system depends on our judgements about whether to reject or accept specific deductive inferences.  Thus, for Goodman, the problem of induction dissolves into the same problem as justifying a deductive system and while, according to Goodman, Hume was on the right track with habits of mind, the problem is more complex than Hume realized.

In the context of justifying rules of induction, this becomes the problem of confirmation of generalizations for Goodman.  However, the confirmation is not a problem of justification but instead it is a problem of precisely defining how evidence confirms generalizations.  It is with this turn that ''grue'' and ''bleen'' have their philosophical role in Goodman's view of induction.

===Projectible predicates===
[[File:US government example for Goodman's new riddle of induction_svg.svg|thumb|500px|US government example for time-dependent predicates: [[List of Presidents of the United States#List of presidents|Before March 1797]], arbitrarily many observations would support both versions of the prediction ''"The [[United States Armed Forces|US forces]] were always [[commander-in-chief#United States|commanded]] by { {{su|p=[[George Washington]]|b=[[President of the United States|the &nbsp; US &nbsp; President]]}} }, hence they will be commanded by him in the future"'', which today is known as { {{su|p=false|b=true}} }, similar to ''"Emeralds were always { {{su|p=grue|b=green}} }, hence they will be so in the future"''.]]
The new riddle of induction, for Goodman, rests on our ability to distinguish ''lawlike'' from ''non-lawlike'' generalizations.  ''Lawlike'' generalizations are capable of confirmation while ''non-lawlike'' generalizations are not.  ''Lawlike'' generalizations are required for making predictions.  Using examples from Goodman, the generalization that all copper conducts electricity is capable of confirmation by a particular piece of copper whereas the generalization that all men in a given room are third sons is not ''lawlike'' but accidental.  The generalization that all copper conducts electricity is a basis for predicting that this piece of copper will conduct electricity.  The generalization that all men in a given room are third sons, however, is not a basis for predicting that a given man in that room is a third son.

The question, therefore, is what makes some generalizations ''lawlike'' and others accidental.  This, for Goodman, becomes a problem of determining which predicates are projectible (i.e., can be used in ''lawlike'' generalizations that serve as predictions) and which are not. Goodman argues that this is where the fundamental problem lies. This problem is known as '''Goodman's paradox''': from the apparently strong evidence that all [[emerald]]s examined thus far have been green, one may inductively conclude that all future emeralds will be green. However, whether this prediction is ''lawlike'' or not depends on the predicates used in this prediction.  Goodman observed that (assuming ''t'' has yet to pass) it is equally true that every emerald that has been observed is ''grue''.  Thus, by the same evidence we can conclude that all future emeralds will be ''grue''.  The new problem of induction becomes one of distinguishing projectible predicates such as ''green'' and ''blue'' from non-projectible predicates such as ''grue'' and ''bleen''.

Hume, Goodman argues, missed this problem.  We do not, by habit, form generalizations from all associations of events we have observed but only some of them. All past observed emeralds were green, and we formed a habit of thinking the next emerald will be green, but they were equally grue, and we do not form habits concerning grueness. ''Lawlike'' predictions (or projections) ultimately are distinguishable by the predicates we use. Goodman's solution is to argue that ''lawlike'' predictions are based on projectible predicates such as ''green'' and ''blue'' and not on non-projectible predicates such as ''grue'' and ''bleen'' and what makes predicates projectible is their ''entrenchment'', which depends on their successful past projections.  Thus, ''grue'' and ''bleen'' function in Goodman's arguments to both illustrate the new riddle of induction and to illustrate the distinction between projectible and non-projectible predicates via their relative entrenchment.